Thallium energy level diagram

Energy levels and transitions of neutral thallium (Tl I): the 18 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 12 levels they connect, each line with its vacuum wavelength, frequency and, for 17 of them, the reduced dipole matrix element derived from the NIST transition rate. Measured lifetimes, transition rates, hyperfine constants and isotope shifts from the literature are included, each with its citation.

Hover a line or a level to isolate it, click to keep it selected. Scroll to zoom, drag to move.

Download: diagram (PDF) diagram (SVG) transitions (CSV) levels (CSV) source code

Key transitions of thallium

λ, ν from NIST level energies unless a measured frequency for this isotope is available. A: measured value or NIST. Γ/2π: natural linewidth of the upper level, 1/(2πτ).

²⁰⁵Tl hyperfine structure (I = 1/2)

Measured A, B constants; sources in the data file.

Isotope shifts

Shift = ν(first isotope) − ν(second isotope).

Closed and nearly closed transitions of thallium

A transition is closed when its upper level can decay only to the level it was excited from, so the atom keeps scattering photons. “closed”: among the levels NIST lists, no other level below the upper level has the opposite parity and |ΔJ| ≤ 1, so no other electric-dipole decay exists. Otherwise the leak is the sum of the branching ratios of the other decay lines of the upper level (or 1 − branching ratio where that of the line itself has been measured), and the number of photons is 1 / leak. “≥” and “≤”: at least one possible decay path has no listed rate, so the leak is a lower limit. These numbers are derived from the branching ratios, lifetimes and rates of this page, not measured as such; the tag names the weakest of the inputs, * marks theory and ≈ a model or semi-empirical calculation. Listed: lines that start on the ground level or on a metastable level and leak at most 10 %, unless more than three possible decay paths have no listed rate. Fine-structure levels only: hyperfine and Zeeman dark states and forbidden decays without a listed rate are not considered. Select a line in the diagram for the full list of its leak channels.

Listed Tl transitions below 2 µm

Reduced dipole matrix elements follow the convention A = ω³|d|²/(3πε₀ħc³(2J′+1)), with J′ the upper level. Tags show where a number comes from: measured, NIST compilation, high-accuracy theory, this site's own Cowan-code calculation with the parameters fitted to the NIST energies (HFR fit; inputs and fit report in the repository folder cowan/; used only where nothing else gives a rate; strong lines typically within a factor 2, weak lines worse), or a model calculation.

Tl energy levels

Tl⁺ ionisation limit 49266.66 cm⁻¹ = 6.10829 eV (202.977 nm)

Sources

• Chen, Fan, Chen, Lin, Chen, Shy, Liu, Phys. Rev. A 86, 052524 (2012) (arXiv:physics/07030…
• Chen, Fan, Chen, Lin, Chen, Shy, Liu, Phys. Rev. A 86, 052524 (2012) (arXiv:physics/07030…
• Gallagher, Lurio, Phys. Rev. 136, A87 (1964) (abstract; level-crossing technique)
• Hunter, Commins, Roesch, Phys. Rev. A 25, 885 (1982) (abstract)
• Lurio, Prodell, Phys. Rev. 101, 79 (1956) (abstract): ground-state hyperfine splitting De…
• NIST ASD
• NIST ASD level energies
• Norton, Gallagher, Phys. Rev. A 3, 915 (1971) (abstract; zero-field level crossing / Hanl…
• Prosnyak, Skripnikov, Phys. Rev. C 103, 034314 (2021) (arXiv:2101.01145), Sec. IV text ("…
• Ranjit, Kealhofer, Vukasin, Majumder, Phys. Rev. A 89, 012511 (2014) (arXiv:1310.7216), T…
• Rupasinghe, Vilas, Hoenig, Wang, Majumder, arXiv:1702.06565 (2017), Table I
• Rupasinghe, Vilas, Hoenig, Wang, Majumder, arXiv:1702.06565 (2017), Table I: hyperfine sp…
• Safronova, Safronova, Johnson, Phys. Rev. A 71, 052506 (2005) (arXiv:physics/0410079), Ta…
• Safronova, Safronova, Johnson, Phys. Rev. A 71, 052506 (2005) (arXiv:physics/0410079), Ta…
• Safronova, Safronova, Johnson, Phys. Rev. A 71, 052506 (2005) (arXiv:physics/0410079), Ta…
• Safronova, Safronova, Johnson, Phys. Rev. A 71, 052506 (2005) (arXiv:physics/0410079), Ta…
• Safronova, Safronova, Johnson, Phys. Rev. A 71, 052506 (2005) (arXiv:physics/0410079), Ta…
• Safronova, Safronova, Johnson, Phys. Rev. A 71, 052506 (2005) (arXiv:physics/0410079), Ta…
• Safronova, Safronova, Johnson, Phys. Rev. A 71, 052506 (2005) (arXiv:physics/0410079), Ta…
• Safronova, Safronova, Johnson, Phys. Rev. A 71, 052506 (2005) (arXiv:physics/0410079), Ta…
• Safronova, Safronova, Johnson, Phys. Rev. A 71, 052506 (2005) (arXiv:physics/0410079), Ta…

I(203Tl) = I(205Tl) = 1/2, so there are no B constants; for J=1/2 levels the hyperfine splitting equals A, for J=3/2 it equals 2A. rme_J_ea0 is |<J||D||J'>| in e*a0 in the Safronova convention A = 2.02613e18 S /((2J'+1) lambda^3[A]) with S = rme^2 (J' = upper level), identical to the schema convention. Entries marked compilation with "Table IV, column Z(expt)" are experimental matrix elements as collected by Kozlov, Porsev, Johnson 2001 and quoted by Safronova et al. 2005. The 7s-7p matrix elements and 7p lifetimes labelled derived come from the measured 378 nm Stark shift combined with theory (Safronova & Majumder 2013). Isotope shifts follow the SCHEMA convention nu(first)-nu(second) where the sign could be verified (378 nm: 205Tl higher); for the IR/red second-step transitions only the magnitude is certain. Extra fields beyond SCHEMA.md: hyperfine_component_frequencies_MHz, hyperfine_component_frequency_MHz, E2_M1_amplitude_ratio, PNC_E1_over_M1, A_E2_s, stark_shift_kHz_per_kVcm2, ionization_energy, mu_N. The UDel portal has no neutral Tl entry (only Tl+); neutral-atom theory comes from the Safronova-group papers.

Atoms with measured data

• Lithium-632 levels, 85 lines
• Lithium-732 levels, 85 lines
• Beryllium-917 levels, 26 lines
• Sodium-2336 levels, 106 lines
• Magnesium-2418 levels, 61 lines
• Magnesium-2518 levels, 61 lines
• Potassium-3934 levels, 84 lines
• Potassium-4034 levels, 84 lines
• Potassium-4134 levels, 84 lines
• Calcium-4035 levels, 61 lines
• Calcium-4335 levels, 61 lines
• Chromium-5256 levels, 87 lines
• Chromium-5356 levels, 87 lines
• Rubidium-8536 levels, 94 lines
• Rubidium-8736 levels, 94 lines
• Strontium-8440 levels, 70 lines
• Strontium-8640 levels, 70 lines
• Strontium-8740 levels, 70 lines
• Strontium-8840 levels, 70 lines
• Cadmium-11115 levels, 21 lines
• Cadmium-11315 levels, 21 lines
• Cadmium-11415 levels, 21 lines
• Caesium-13331 levels, 79 lines
• Barium-13744 levels, 89 lines
• Barium-13844 levels, 89 lines
• Dysprosium-16139 levels, 55 lines
• Dysprosium-16239 levels, 55 lines
• Dysprosium-16339 levels, 55 lines
• Dysprosium-16439 levels, 55 lines
• Erbium-16673 levels, 90 lines
• Erbium-16773 levels, 90 lines
• Erbium-16873 levels, 90 lines
• Thulium-16972 levels, 73 lines
• Ytterbium-17118 levels, 26 lines
• Ytterbium-17318 levels, 26 lines
• Ytterbium-17418 levels, 26 lines
• Mercury-19927 levels, 47 lines
• Mercury-20127 levels, 47 lines
• Mercury-20227 levels, 47 lines

All elements: periodic table